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Question

  • A hawk is flying horizontally at 10 m/s in a straight line, 200 m above the ground. A mouse it has been carrying struggles free from its grasp. The hawk continues on its path at the same speed for 2 seconds before attempting to retrieve its prey. To accomplish the retrieval, it dives in a straight line at constant speed and recaptures the mouse 3 m above the ground. (a) Assuming no air resistance, find the diving speed of the hawk.

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Solution

Time interval of fall:t=2hg =2×gVertical distance travelled:y=200 - 3 = 197 mTime interval of fall:t=2yg =2×1979.8 =6.34 sHorizontal distance travelled by the hawk:x=vT =vt-2 =10×4.34 =43.4 mTotal distance travelled by hawk:d=x2+y2 =43.42+1972 =202 mDiving speed:vdiving=dT =20243.4 =46.5 m/s

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